Potentials and Limits to Basin Stability Estimation

Abstract

Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. This requires numerical estimation via Monte-Carlo sampling and integration of differential equations. Here, we analyze the applicability of basin stability to systems with basin geometries challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.

5 pages, 4 figures

References in corpus (1)

• Building blocks of the basin stability of power grids

Cited by in corpus (15)

• The Size of the Sync Basin Revisited
• Deciphering the imprint of topology on nonlinear dynamical network stability
• Perpetual points: New tool for localization of co-existing attractors in dynamical systems
• Multistability and Variations in Basin of Attraction in Power-grid Systems
• Riddling: Chimera's dilemma
• Bounding the first exit from the basin: Independence Times and Finite-Time Basin Stability
• Framework for global stability analysis of dynamical systems
• On structural and dynamical factors determining the integrated basin instability of power-grid nodes
• Dynamics of Nonlinear Random Walks on Complex Networks
• Decreased resilience in power grids under dynamically induced vulnerabilities
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• System Size Identification from Sinusoidal Probing in Diffusive Complex Networks
• Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter
• The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system
• Basins with tentacles